I am looking into a laptop that would support gaming (specifically for D3, LoL, SC2 and such) for my brother, as I have no idea what would be a good laptop, it would be great if you guys can give me some advice and suggestions! My price range is *hopefully* between 750-850 if plausible.

Hmmm... in that price range the HP dv6t Quad is very solid for gaming, and the regular dv6t with a 3rd gen Intel Core i5 and dedicated graphics is good for a bit less money. The Sony Vaio S 15.5 is also a good choice.